For the last part, you have to find where 
attains its maximum over 
. We have
so that
with critical points at 
such that
So either
or
where 
is any integer. We get 8 solutions over the given interval with 
from the first set of solutions, 
from the set of solutions where 
, and 
from the set of solutions where 
. They are approximately
Answer:
G = kX
Where:
G - Growth rate
X = the initial/current population of rabbit
k = is the constant of proportionality.
Step-by-step explanation:
As we are told in the question, the growth rate is proportional to the current population. This information gives us the initial value needed to solve to find the population of rabbits at any given time.
Other information given as needed for computation and we are not asked to do anything further.
<u>Analytically,</u>
If X = 100
And it triples in 2 years. That is, 3*X = 300. 2 years is 24 months.
This gives us the monthly growth rate = 300/24 = 12.5 => 12 to 13 rabbits per months.
Foxes kill 2 rabbits per month. This implies that 2*24 = 48 rabbits are killed by Foxes in 24 months.
By implication, the population of rabbits in 2 years will be
X (in 2 years) = 300 - 48 = 252 rabbits.
2 of three would be the answer
